Macroscopic Forcing Method with Restricted Nonlinear Advection

The macroscopic forcing method (MFM) is a systematic approach that can highlight important anisotropic and non-local turbulence mixing effects in turbulent flows. The method has the potential to inform eddy viscosity closures for Reynolds-averaged Navier-Stokes (RANS) simulations, but its need for extensive direct numerical simulation (DNS) data to obtain the desired eddy viscosity kernel poses computational challenges. To alleviate this computational burden, we propose the use of a reduced-order model rather than the full Navier Stokes equations to advect the generalized momentum transport (GMT) equations in the MFM framework. In particular, we use the restricted nonlinear (RNL) model due to its proven ability to resolve the coherent structures essential to wall-turbulent mixing. This presentation will illustrate the RNL-MFM framework and highlight the extent to which this reduced representation of streamwise coherent structures can inform RANS closures. In particular, we will demonstrate that using only the large-scale (streamwise-averaged mean component) to inform the MFM leads to accurate predictions of key components of the eddy viscosity kernel with significant computational savings. However, introducing the RNL small-scales (streamwise-varying perturbations) leads to improved eddy viscosity closure predictions but introduces increases in complexity. Trade-offs between computational cost versus eddy viscosity closure fidelity will be discussed.